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Is $x^{2} + y^{2} = 9$ $x^2+y^2=9$ a function?

1 Answer

Aug 1, 2015

$x^{2} + y^{2} = 9$ $x^2+y^2 = 9$ is not a function

Explanation:

In order for an equation to represent a function any single value of $x$ $x$ must have at most one corresponding value of $y$ $y$ which satisfies the equation.

For $x^{2} + y^{2} = 9$ $x^2+y^2=9$
$XXXX$ $color(white)("XXXX")$ if (for example) $x = 0$ $x=0$
$XXXX$ $color(white)("XXXX")$ there are two values for $y$ $y$ (namely $+ 3$ $+3$ and $- 3$ $-3$ ) which satisfy the equation

and therefore the equation is not a function.

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